We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like operators defined on a Banach space. As corollaries, the results show that the Jungck-Mann, Jungck-Ishikawa and Jungck-Noor iterations can also be used to approximate the common fixed points of such maps. The results are imp...

In this paper, we consider an algebraic additive Schwarz iteration scheme for solving the nite-dimensional linear complementarity problem that involves an M-matrix. The scheme contains some existing algorithms as special cases. We establish monotone convergence of the iteration scheme under appropriate conditions. Moreover, using the concept of weak regular splitting, we estimate weighted max-n...

A new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric mean of two Hermitian positive definite matrices is constructed. Moreover, another efficient algorithm for this purpose is derived free from the computation of principal matrix...

X. Qin and Y. Su proved a strong convergence theorems of modified Ishikawa iteration by CQ method for relatively nonexpansive mappings in a Banach space [Xiaolong Qin, Yongfu Su, Nonlinear Anal. 67 (2007), no. 6, 1958–1965]. The result of this paper extends and improves the result of X. Qin and Y. Su in the two respects: (1). By using the monotone CQ method to modify the CQ method, so that the ...

In this paper, an iterative incremental relay selection (IIRS) scheme is considered for wireless cooperative networks in order to increase the reliability of transmission. Different from the conventional incremental relay selection which incrementally selects a best relay for only one iteration; the IIRS scheme iteratively applies the incremental relaying and relay selection processes. To evalu...

In this paper, a new iteration scheme in uniformly convex metric space is defined and its convergence obtained. A numerical example also considered to compare the rate of convergences with that an existing scheme.

In this paper, we prove weak and strong convergence of the Ishikawa iterative scheme with errors to common fixed point I-asymptotically quasinonexpansive mappings in a Banach space. The results obtained in this paper improve and generalize the corresponding results in the existing literature.